Equation of state for insoluble monolayers of aggregating amphiphilic molecules

For Langmuir monolayers at the air-water interface, an equation of state is theoretically derived which describes the main phase transition between the gaslike and the condensed phases. The theoretical treatment considers the formation of two-dimensional aggregates and describes the nonhorizontal phase transition of the surface pressure-area isotherms and its dependence on the temperature. The equilibrium between the aggregates and monomers was treated using Buttler's equation for the chemical potential of monomers and aggregates within the surface. The results predicted by the theory agree well with the experimental surface pressure-area isotherms over a large temperature range.